If your insurance is paying for the quarter panels, then you can definitely turn some lemons into gold. That's the hardest and most expensive part of a 1M conversion.

If you're just doing the rear end, then the side skirts will also be a challenge. The stock 135i skirts won't match up with the 1M parts, and the 1M skirts won't match up with the factory 135i front end. You'd have to splice your factory 135i skirt with a 1M skirt to produce a hybrid that'll fit your 135i front end and your 1M back end. Somebody did it recently (except the opposite - 135 back, 1M front)... the body shop guy apparently told him that the splice job was 20 hours on its own.

yes,
the rear end is the greatest challenge. Do note, if you only do the rear end with the OEM bumper, you will have to Mod your rear quarters and sideskirts as the flat rim (quarter panel) around the wheel well is thinner on the 1M. your 135i is considerably thicker. It looks ok when only the front end is widened as the thicker rear rim is forgiving. It would look awkward with the thin rear and a thick front. If you do the rear, you might as well do the front too as you would already be doing the most expensive and difficult work.

You will also have to modify your battery tray to fit a true 1M exhaust or have a custom exhaust made.